Problem: A circle with circumference $12\pi$ has an arc with a $\dfrac{7}{6}\pi$ radians central angle. What is the length of the arc? {12\pi} {\dfrac{7}{6}\pi} \color{#DF0030}{7\pi}
Solution: The ratio between the arc's central angle $\theta$ and $2 \pi$ radians is equal to the the ratio between the arc length $s$ and the circle's circumference $c$ $\dfrac{\theta}{2 \pi} = \dfrac{s}{c}$ $\dfrac{7}{6}\pi \div 2 \pi = \dfrac{s}{12\pi}$ $\dfrac{7}{12} = \dfrac{s}{12\pi}$ $\dfrac{7}{12} \times 12\pi = s$ $7\pi = s$